Problem:
Consider the parallelogram with vertices , and . A line through the origin cuts this figure into two congruent polygons. The slope of the line is , where and are relatively prime positive integers. Find .
Solution:
The line must go through the point where the diagonals of the parallelogram bisect each other, namely . Thus the slope of the line is , and .
The problems on this page are the property of the MAA's American Mathematics Competitions